🤯 AI Breakthrough: Math's Ancient Puzzle Solved! 🚀

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ChatGPT’s Unexpected Mathematical Breakthrough
Neel Somani, a software engineer with a background as a former quant researcher and startup founder, made a surprising discovery while testing OpenAI’s new model. After inputting a complex mathematical problem into ChatGPT and allowing it to “think” for 15 minutes, he returned to a complete solution. He then evaluated and formalized the proof using the tool Harmonic, confirming its accuracy. “I was interested in establishing a baseline for when large language models effectively solve open math problems compared to where they typically struggle,” Somani explained.

A New Era of AI-Assisted Mathematics
The sudden increase in solved Erdős problems is less important than the fact that leading mathematicians and computer science professors are beginning to utilize these tools. These individuals have reputations to uphold, and when they are openly using Aristotle or ChatGPT, that represents substantial validation. The development of tools like Lean, an open-source “proof assistant” developed at Microsoft Research in 2013, is dramatically streamlining the process of formalizing mathematical reasoning.

ChatGPT’s ‘Chain of Thought’ Demonstrated
Notably, ChatGPT demonstrated an impressive “chain of thought,” articulating mathematical axioms such as Legendre’s formula, Bertrand’s postulate, and the Star of David theorem. Furthermore, the model identified a 2013 Math Overflow post by Harvard mathematician Noam Elkies, presenting an elegant solution to a similar problem. However, ChatGPT’s final proof differed significantly from Elkies’ work, ultimately offering a more comprehensive solution to a problem posed by the legendary mathematician Paul Erdős – a challenge whose vast collection of unsolved problems has served as a proving ground for artificial intelligence.

Formalization: A Key Driver of AI’s Progress
The shift in mathematical problem-solving is increasingly led by a process called formalization, which, though labor-intensive, significantly simplifies mathematical reasoning and allows for easier verification and extension. A key driving force behind this trend is a recent move toward formalization, a process that, though labor-intensive, significantly simplifies mathematical reasoning and allows for easier verification and extension. Harmonic’s Aristotle, an AI tool promising to automate much of the formalization work, is also gaining significant traction.

AI’s Growing Reach into the ‘Long Tail’
Systematically applied to the ‘long tail’ of obscure Erdős problems – many of which actually possess straightforward solutions – this shift is increasingly leading to the use of purely AI-based methods for their resolution. The sudden increase in solved Erdős problems is less important than the fact that leading mathematicians and computer science professors are beginning to utilize these tools. These individuals have reputations to uphold, and when they are openly using Aristotle or ChatGPT, that represents substantial validation.

A Validation of AI’s Potential
The scalable nature of these AI systems makes them “better suited for being”

This article is AI-synthesized from public sources and may not reflect original reporting.